Paradox: I work in Adobe RGB with a wide-gamut monitor. Once finished with a photo and when I want an sRGB version, I put the NEC PA monitor back to sRGB and do a Change Profile twice for comparison, once with Maintain Full Gamut and once with Preserve Identical Colors Plus Black Point Compensation. Depending on the particular photo, the difference might be indistinguishable, subtle, or obvious. However, whenever I Composite the two sRGB images using Absolute Difference, the result is all black.

Composite should give you a warning if the two images are in different color spaces.

Depending on how you convert from AdobeRGB to sRGB, the results can be different. In this case you should change both the profile and the image data since simply re-tagging the image with a new profile or simply transforming the image data will cause a color shift. Unless you transform the image data, there should not be a difference when you subtract the images.

In any case, when using Composite you need to make sure the Overlay Amount is set to 100% to see the difference.

The Difference transformation should also give you a profile mismatch warning when comparing images in different color spaces.

Yes, I followed all the settings you specify. So what explains the paradox that the two sRGB results look different to my eye but the Absolute Difference, or Subtract for that matter, is black, and Readouts, 1 x 1 pixel, from random locations around the image are all 0,0,0?

As I understand it, the ability to handle different rendering intents is optional, depending on the profile. Monitor profiles and color space profiles such as sRGB generally ignore this setting as it is primarily intended for printer profiles. Depending on the printer profile, it may still ignore the rendering intent. When I do it here, both images look the same. Do you have a proofing profile enabled?

Same result for the sRGB conversion whether a proofing profile is enabled or not. However, your reply prompted me to save both sRGB conversions of a photo, open Fast Stone, and toggle between them, one on top of the other, so to speak -- no difference discernible! I guess my eyes and brain fool themselves in side-by-side comparison of two windows in PWP. Maybe it is the same optical illusion based on surrounding color as in the attached file, where A and B are identical, only not so strong.

Even good monitors have minor variations in brightness and color from one side to the other. In addition there are often slight variations in appearance with viewing angle. For this reason and also because you bring the eye's motion detectors into play, the blink test is the best way to see visual differences between two images. To tell if two images are the same digitally, you can take the absolute (or offset) difference and then expand to full range using Levels and Color. This will magnify even the slightest variations.

Incidentally, a similar technique is useful to test for dust on your sensor - choose the smallest aperture you can and take a defocused photo of clear blue sky or a white sheet of paper. Then expand to full range using Levels and Color and any imperfections should show up clearly.